Simplify the following expression: $\dfrac{42k^5}{36k^3}$ You can assume $k \neq 0$.
Answer: $ \dfrac{42k^5}{36k^3} = \dfrac{42}{36} \cdot \dfrac{k^5}{k^3} $ To simplify $\frac{42}{36}$ , find the greatest common factor (GCD) of $42$ and $36$ $42 = 2 \cdot 3 \cdot 7$ $36 = 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(42, 36) = 2 \cdot 3 = 6 $ $ \dfrac{42}{36} \cdot \dfrac{k^5}{k^3} = \dfrac{6 \cdot 7}{6 \cdot 6} \cdot \dfrac{k^5}{k^3} $ $\phantom{ \dfrac{42}{36} \cdot \dfrac{5}{3}} = \dfrac{7}{6} \cdot \dfrac{k^5}{k^3} $ $ \dfrac{k^5}{k^3} = \dfrac{k \cdot k \cdot k \cdot k \cdot k}{k \cdot k \cdot k} = k^2 $ $ \dfrac{7}{6} \cdot k^2 = \dfrac{7k^2}{6} $